Geometric Structure of Generation Mixing: Qualitative Derivation of CKM and PMNS Matrices

Key Points

• To provide a structural explanation for the generation mixing problem using the S_3 permutation symmetry.
• Derived qualitative structures based on S_3 symmetry of three generations.
• Examined the breaking pattern of the symmetry in relation to particle generation.
• The hierarchical structure of CKM and PMNS matrices is qualitatively reproduced.
• S_3 symmetry offers insight into the organization of particle generations.